In a large bowl or baking dish, combine Greek yogurt, mustard and garlic. The Greek yogurt might be stiff if cold, so work well to combine.
Add chicken and coat evenly in the yogurt mixture.
Cover the entire dish with plastic wrap and refrigerate for at least 8 hours or overnight.
Once the chicken has rested, preheat the oven to 425° F. Prepare a baking sheet with oil and set aside.
In another medium bowl or baking dish, mix together the flour, paprika, baking powder, salt and pepper. Use a whisk or fork to ensure the seasonings are distributed in the mixture.
Remove chicken from yogurt marinade one piece at a time. Add to seasoning mixture and toss to coat completely.
Place coated chicken pieces on a wire rack over the prepared baking sheet.
Once all chicken drumsticks are coated in batter, bake for 40 to 45 minutes, checking to see if the outside of the chicken is a deep golden brown. Use a meat thermometer to see that chicken is at 170°-175° F before serving.